Math Chapters 1-4 Variables in Algebra 1.1 -
Variable-expression or equation with a letter
Evaluating-the number answer
Verbal Model-math to english
Speed=Distance/Time
Examples-89 miles in 2 hours speed?
89/2 = 44.5 mph
Interest Problems-PRT
P=principle
R=rate
T=time
Example- $8.70, 2years, 5% interest
(870)(.05)(2)= $87 1.2 Exponents & Powers :
Area of a square (S*S or S squared) *square units*
Volume of a Cube (S*S*S or S cubed) *units cubed* 1.3 Order of Operations : Steps:
1.Parentheses
2. Exponents
3. Multiply/Divide (left to right)
4.Add/Subtract (left to right)
Ex) 32-16+2
16+2=18 1.4 Equations & Inequalities :
Equation-has an equal sign.
Open Sentence-has a variable.
Solution of an Equation-number that makes the equation true.
Solving-finding the number that makes it work.
Inequality- ><
Solution of an Inequality-number(s) that makes the inequality true.
Ex) 2x+7=13 ; 3 or 4 The right answer is 3. 1.5 Translating verbal Phrases into Algebraic Expressions :
Eight less than half of a number = 1/2n - 8
Product of ten and a number = n - 5 1.7 Into to Functions :
Function-a rule that establishes a relationship.
Domain- input values (x values)
Range-output values (y values) 2.1 Day 2 :
Key Terms
-opposite
-absolute value
-counterexample
-number line
-zero
-positive
-negative
Absolute Value-The absolute value of a number is its distance from zero
on the number line.Absolute values are always positive and the absolute
value of a positive number is a positive number.The absolute value of a
negative number is a positive number. 2.2 Addition of Real Numbers :
Commutative- move pieces around and get the same answer.
Associative-grouping.
Identity- add zero.
Inverse- add the opposite. 2.3 Subtraction of Real Numbers :
Put in ( ) ....pick up signs in front .
Ex) (-12)+(-7)=(-19) 2.4 Adding & Subtracting Matrices :
Matrix-a way to collect/display data.
*rectangular array or elements.
*rows and columns made up of entries. 2.5 Multiplication of Real Numbers :
Commutative-move.
Associative-grouping.
Identity-multiply by one.
Zero-multiply by zero.
Property of Opposites-multiply by negative one
*In multiplication if you have different signs the product will be negative*
*In multiplication if you have the same signs the product will be positive* 2.6 Distributive Property :
Objective-utilize the distributive property and simplify expressions by
combining like terms.
Key terms: Coefficient,Term,Like terms,Constant Term,Commutative Property of X 2.7 Division of Real Numbers :
Sign Rule-if your are dividing two numbers with the same sign the
quotient is positive and if dividing two numbers with different signs
the quotient is negative. 3.4 Solving Equations with Variables on Both Sides : Steps :
1.Distribute to remove parentheses.
2.Add like terms on either side of the equation.
3.Move the variables to the same side of the equation by addition or subtraction.
4.Move the constants to the same side of the equation by addition or subtraction.
5.Divide by the coefficient of x or multiply the reciprocal of the coefficient. Ratios & Rates :
-Ratios compare quantities measured in the same units
-Ratio of A to B..... A/B 4.1 Coordinates & ScatterPlots
Coordinate Plane- two number lines that intersect at a right angle.
Ordered Pair-a point on the coordinate plane (x,y)
ScatterPlot-a graph containing several points that represent data. 4.2 Graphing Linear Equations :
Solution-answer that makes our equation true or equal.
Steps to Graph :
1.Get y alone. (function form)
2.Make an x/y table (3 values)
3.Plot your points on the graph.
4.Connect the points straight. 4.3 Quick Graphs with Intercepts :
x-intercept-where the graph crosses the x-axis.
y-intercept-where the graph crosses the y-axis
Steps to Graph with Intercepts :
1.Let y=0 and find the x intercept.
2.Let x=0 and find the y intercept.
3.Plot & connect. 4.4 Slope of a Line :
Slope-steepness of a line,rate of change between two points,m,rise/run,and change in y/change in x . 4.6 Slope-Intercept Form of a Line :
-the linear equation y=mx+b is slope intercept form.
Steps to Graph :
1.Find m and the y-intercept.
2.Graph the y-intercept.
3.From y-intercept,rise /run.
4.Connect the points.
*Parallel lines have the same slope* 4.8 Functions & Relations :
Relation-any set of ordered pairs.
Function-a relation in which each input has exactly one output.
Domain=x values and input.
Range=y values and output.
Variables in Algebra 1.1 -
Variable-expression or equation with a letter
Evaluating-the number answer
Verbal Model-math to english
Speed=Distance/Time
Examples-89 miles in 2 hours speed?
89/2 = 44.5 mph
Interest Problems-PRT
P=principle
R=rate
T=time
Example- $8.70, 2years, 5% interest
(870)(.05)(2)= $87
1.2 Exponents & Powers :
Area of a square (S*S or S squared) *square units*
Volume of a Cube (S*S*S or S cubed) *units cubed*
1.3 Order of Operations :
Steps:
1.Parentheses
2. Exponents
3. Multiply/Divide (left to right)
4.Add/Subtract (left to right)
Ex) 32-16+2
16+2=18
1.4 Equations & Inequalities :
Equation-has an equal sign.
Open Sentence-has a variable.
Solution of an Equation-number that makes the equation true.
Solving-finding the number that makes it work.
Inequality- ><
Solution of an Inequality-number(s) that makes the inequality true.
Ex) 2x+7=13 ; 3 or 4 The right answer is 3.
1.5 Translating verbal Phrases into Algebraic Expressions :
Eight less than half of a number = 1/2n - 8
Product of ten and a number = n - 5
1.7 Into to Functions :
Function-a rule that establishes a relationship.
Domain- input values (x values)
Range-output values (y values)
2.1 Day 2 :
Key Terms
-opposite
-absolute value
-counterexample
-number line
-zero
-positive
-negative
Absolute Value-The absolute value of a number is its distance from zero
on the number line.Absolute values are always positive and the absolute
value of a positive number is a positive number.The absolute value of a
negative number is a positive number.
2.2 Addition of Real Numbers :
Commutative- move pieces around and get the same answer.
Associative-grouping.
Identity- add zero.
Inverse- add the opposite.
2.3 Subtraction of Real Numbers :
- Put in ( ) ....pick up signs in front .
Ex) (-12)+(-7)=(-19)2.4 Adding & Subtracting Matrices :
Matrix-a way to collect/display data.
*rectangular array or elements.
*rows and columns made up of entries.
2.5 Multiplication of Real Numbers :
Commutative-move.
Associative-grouping.
Identity-multiply by one.
Zero-multiply by zero.
Property of Opposites-multiply by negative one
*In multiplication if you have different signs the product will be negative*
*In multiplication if you have the same signs the product will be positive*
2.6 Distributive Property :
Objective-utilize the distributive property and simplify expressions by
combining like terms.
Key terms: Coefficient,Term,Like terms,Constant Term,Commutative Property of X
2.7 Division of Real Numbers :
Sign Rule-if your are dividing two numbers with the same sign the
quotient is positive and if dividing two numbers with different signs
the quotient is negative.
3.4 Solving Equations with Variables on Both Sides :
Steps :
1.Distribute to remove parentheses.
2.Add like terms on either side of the equation.
3.Move the variables to the same side of the equation by addition or subtraction.
4.Move the constants to the same side of the equation by addition or subtraction.
5.Divide by the coefficient of x or multiply the reciprocal of the coefficient.
Ratios & Rates :
-Ratios compare quantities measured in the same units
-Ratio of A to B..... A/B
4.1 Coordinates & ScatterPlots
Coordinate Plane- two number lines that intersect at a right angle.
Ordered Pair-a point on the coordinate plane (x,y)
ScatterPlot-a graph containing several points that represent data.
4.2 Graphing Linear Equations :
Solution-answer that makes our equation true or equal.
Steps to Graph :
1.Get y alone. (function form)
2.Make an x/y table (3 values)
3.Plot your points on the graph.
4.Connect the points straight.
4.3 Quick Graphs with Intercepts :
x-intercept-where the graph crosses the x-axis.
y-intercept-where the graph crosses the y-axis
Steps to Graph with Intercepts :
1.Let y=0 and find the x intercept.
2.Let x=0 and find the y intercept.
3.Plot & connect.
4.4 Slope of a Line :
Slope-steepness of a line,rate of change between two points,m,rise/run,and change in y/change in x .
4.6 Slope-Intercept Form of a Line :
-the linear equation y=mx+b is slope intercept form.
Steps to Graph :
1.Find m and the y-intercept.
2.Graph the y-intercept.
3.From y-intercept,rise /run.
4.Connect the points.
*Parallel lines have the same slope*
4.8 Functions & Relations :
Relation-any set of ordered pairs.
Function-a relation in which each input has exactly one output.
Domain=x values and input.
Range=y values and output.